Rega, Levinson or other Integrated for Avalon Eidelon Diamond

Go with the Mark Levinson No. 5805.

Your Avalons are ~85–87 dB “true” sensitivity with a 3.8 Ω minimum and a 6 Ω average load—so they like current + control. 

The 5805 gives you a serious MC/MM phono stage onboard (MC gain ~69 dB with selectable loading 37–1000 Ω; MM gain ~39 dB with selectable capacitance) and stout power (125 W/8 Ω, rated to 4 Ω) with proper damping—exactly what a Lyra Delos–type MC needs. 5805 is the cleanest, safest bet within your budget

Alternatively... Parasound Halo HINT 6, Luxman L-509X, Aesthetix Mimas ...

I think your speakers would enjoy this Hegel H390 and Allnic H1201…

https://www.usaudiomart.com/details/650251530-hegel-h390/

https://www.usaudiomart.com/details/650236820-allnic-h-1201-phono-stage/

Thanks for the suggestions! I will do some research on them. I know Levinson is high end brand but any feedback on their reliability? I had a power amp (forget the model) that had to be serviced before I bought it. Never gave me any issues while I had it. I also see several open box and B stock Levinson's on Music Direct, etc. 

I remember a few threads regarding 5805's failing.  Not sure if they have resolved that issue but here is one of those discussions.

https://forum.audiogon.com/discussions/levinson-5805?highlight=5805

If I were integrated shopping I would also add Pass labs to consideration.  If you're buying used there are LOTS of great options listed here for sale. 

Add Coda CSIB to your list. Amazing integrated amp. Drove my Wilson Sabrina no issues. Great sound. 
https://www.usaudiomart.com/details/650239771-mint-3yr-old-coda-csib-integrated-black-v1/

V1: 150 Watts @ 8Ω

300 Watts @ 4Ω

Class A to ~18W @ 8Ω

Maximum Current: 130 Amperes peak